The purpose of this project is to improve the remission induction rate of acute lymphocytic leukemia in adult patients utilizing vincristine and dexamethasone with intermittent moderate doses of methotrexate followed by L'asparaginase. A second objective is to decrease the incidence of severe infections during induction therapy by utilizing oral non-absorbable antibiotics. A third objective is to determine whether intermittent high dose methotrexate with leucovorin rescue and with vincristine and dexamethasone will prolong remission duration. The fourth objective is to determine the efficacy of moderate and high dose methotrexate in preventing meningeal leukemia and to correlate the clinical effectiveness with the cerebrospinal fluid methotrexate levels. To date 13 patients have been entered onto this study. Seven patients had no prior treatment, six had prior treatment. For the prior treatment patients, one is too early to evaluate, six have been through or are currently on induction, two are on consolidation, one cytoreduction and one is out to maintenance. For the no prior treatment patients, one is too early to evaluate, five have been through or are currently on induction, two are on consolidation, one cytoreduction and one is out to maintenance. For the no prior treatment patients, complete remissions have been acheived in five of six patients that went through induction. For the prior treatment patients, three achieved complete remission and three died.